Tiêu chuẩn iso 18555 2016

INTERNATIONAL
STANDARD

ISO
18555
First edition
2016-02-01

Metallic and other inorganic
coatings — Determination of thermal
conductivity of thermal barrier
coatings
Revêtements métalliques et autres revêtements inorganiques —
Détermination de la conductivité thermique des revêtements
barrières thermiques

Reference number
ISO 18555:2016(E)
© ISO 2016


ISO 18555:2016(E)

COPYRIGHT PROTECTED DOCUMENT
© ISO 2016, Published in Switzerland

All rights reserved. Unless otherwise specified, no part o f this publication may be reproduced or utilized otherwise in any form
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written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country o f

the requester.

ISO copyright o ffice

Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. +41 22 749 01 11
Fax +41 22 749 09 47

www.iso.org

ii

© ISO 2016 – All rights reserved


ISO 18555:2016(E)

Contents

Page

Foreword ........................................................................................................................................................................................................................................ iv
Introduction .................................................................................................................................................................................................................................. v
1
Scope ................................................................................................................................................................................................................................. 1
2
Normative references ...................................................................................................................................................................................... 1
3
Terms and definitions ..................................................................................................................................................................................... 1
4

Principle ........................................................................................................................................................................................................................ 4
5
Apparatus for measuring thermal diffusivity ........................................................................................................................ 4
6
Specimen....................................................................................................................................................................................................................... 5
6.1 Shape and dimensions ...................................................................................................................................................................... 5
6.2 Surface treatment ................................................................................................................................................................................. 7
7
Measuring procedure ...................................................................................................................................................................................... 7
7.1 Specimen thickness ............................................................................................................................................................................. 7
.............................................................................................................................................................................. 7
ff
7.2.1 Measurement of temperature-rise curve.................................................................................................... 7
....................................................................................... 7
f
ff
f
7.2.3 Calculation of thermal diffusivities of BC and TC ................................................................................ 7
..................................................................................................................................................................... 10
............................................................................................................................................................................................ 10
8
Thermal conductivities of BC and TC ........................................................................................................................................... 11
9
Report ........................................................................................................................................................................................................................... 11
9.1 Items to be reported ........................................................................................................................................................................ 11
9.2 Additional items to be selected for the report .......................................................................................................... 12
Annex A (informative) Areal heat diffusion time method ........................................................................................................... 13
Annex B (informative) Examples of theoretical temperature-rise curves ................................................................. 16
Bibliography ............................................................................................................................................................................................................................. 18
7.2

Thermal di

7.2 .2

us ivity

C alculatio n o

7.3

S p ecific heat cap acity

7.4

B ulk dens ity

© ISO 2016 – All rights reserved

thermal di

us ivity o

s ub s trate

iii


ISO 18555:2016(E)

Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work o f preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters o f
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
di fferent types o f ISO documents should be noted. This document was dra fted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some o f the elements o f this document may be the subject o f
patent rights. ISO shall not be held responsible for identi fying any or all such patent rights. Details o f
any patent rights identified during the development o f the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www.iso.org/patents).

Any trade name used in this document is in formation given for the convenience o f users and does not

constitute an endorsement.

For an explanation on the meaning o f ISO specific terms and expressions related to con formity

assessment, as well as information about ISO’s adherence to the WTO principles in the Technical
Barriers to Trade (TBT) see the following URL: Foreword - Supplementary in formation
The committee responsible for this document is ISO/TC 107, Metallic and other inorganic coatings.

iv

© ISO 2016 – All rights reserved


ISO 18555:2 016(E)

Introduction

Thermal barrier coatings are highly advanced material systems. They are generally applied to sur faces
o f hot-section components made o f nickel or cobalt-based superalloys, such as combustors, blades,

vanes of power-generation gas turbines in thermal power plants and aero-engines operated at elevated
temperatures.
The function of these coatings is to protect metallic components for extended periods at elevated

temperatures by employing thermally insulating materials which can sustain an appreciable
temperature di fference between load bearing alloys and coating sur faces. These coatings permit the
high-temperature operation by shielding these components, thereby extending their lives.
Although thermal conductivity is one o f the most important properties o f thermal barrier coatings,
the existing International Standard (ISO 18755:2005) includes only the method for determining the
thermal di ffusivity o f monolithic ceramics, regarding the heat conduction in thermal barrier coating.

© ISO 2016 – All rights reserved

v

INTERNATIONAL STANDARD

ISO 18555:2016(E)

Metallic and other inorganic coatings — Determination of
thermal conductivity of thermal barrier coatings
1 Scope
T h i s I nternationa l Sta ndard s p e ci fie s the me tho d

for de term i n i ng the

therma l conduc tivitie s o f therma l

barrier coatings consisting of metallic bond coats and ceramic top coats, in a direction normal to the
coating surface, at room temperature.

2 Normative references
T he

fol lowi ng

i nd i s p en s able

do c u ments , i n whole or i n p ar t, are normatively re ference d i n th i s do c u ment a nd are

for

its

appl ic ation .

For date d re ference s ,

on ly the

e d ition

cite d appl ie s .

For u ndate d

re ference s , the late s t e d ition o f the re ference d do c u ment (i nclud i ng any amend ments) appl ie s .

ISO 1463, Metallic and oxide coatings — Measurement of coating thickness — Microscopical method
ISO 18755:2005, Fine ceramics (advanced ceramics, advanced technical ceramics) — Determination of

thermal diffusivity of monolithic ceramics by laser flash method

EN 821-3, Advanced technical ceramics — Monolithic ceramics.
Determination of specific heat capacity

Thermophysical properties — Part 3:

ASTM E1269-11, Standard Test Method for Determining Specific Heat Capacity by Differential Scanning
Calorimetry

3 Terms and definitions
Fo r

the

purpose

fo l l o w i n g

o f th i s

s ta nd a rd ,

the

te r m s

a nd

de fi n i tio n s

g i ve n

in

ISO 18755:2005 and the

ap p l y.

3.1
thermal barrier coating
TBC
f
heat transfer from outside of the top coat through the coating to the substrate

two -l ayer co ati ng con s i s ti ng o

N o te 1 to entr y: S e e

a me ta l l ic b ond co at (B C ) a nd a ceram ic top co at ( TC ) , i n order to re duce

Figure 1.

© ISO 2016 – All rights reserved

1


ISO 18555:2016(E)

Key

1
2
3
4

top coat (TC)
bond coat (BC)
substrate
thermal barrier coating (TBC)
Figure 1 — Diagrammatic view of a section of TBC

[S O U RC E : I S O 141 8 8 : 2 01 2 , defi n ition 3 .1 , mo d i fie d]

3.2
apparent thermal diffusivity
therma l d i ffu s ivity o f the s p e c i men s [s ub s trate with b ond co at (B C ) a nd s ub s trate with therma l b arrier
co ati ng ( T B C ) ] i n a d i re c tion norma l to the co ati ng s u r face

3.3
normalized temperature rise
T(t)/ΔT

va lue wh ich i s de term i ne d b y d ivid i ng the d i fference b e twe en the temp eratu re o f the s p e c i men re ar

surface after the pulse heating and the temperature of the specimen rear surface before the pulse
ff
f
f
temperature of the specimen rear surface before the pulse heating
he ati ng by the d i

erence b e twe en the ma xi mu m temp eratu re o

the s p e ci men re ar s ur ace a nd the

T(t ) = T (t ) − T
∆T T − T
1

where

0

max

1( )

T t

i s temp eratu re o f s p e ci men re ar s ur face a fter pu l s e he ati ng b y a fla sh me tho d;

t

i s ti me;

0

T

max

T

i s temp erature o f the s p e c i men re ar s u r face b e fore pu l s e he ati ng;

is maximum temperature of specimen rear surface.

N o te 1 to entr y: S e e

2

0

Figure 2.

© ISO 2016 – All rights reserved


ISO 18555:2016(E)

a) Flash method
Key

1
2
3
4
5
6
7

pulse heating
specimen
substrate
TBC
front surface
rear surface
infrared radiometer

b) Temperature-rise curve under ideal conditions

X time (s)
Y normalized temperature rise T(t

A areal heat diffusion time (s)

) / Δ

T

Figure 2 — Flash method and temperature-rise curve under ideal conditions
3.4
temperature-rise curve

curve which shows the variation in the normalized temperature rise of the specimen rear surface with
time
N o te 1 to entr y: S e e the th ick s o l id l i ne i n

Figure 2b.

3.5
half rise-time

1/2

t

time required for the normalized temperature rise to reach 0,5 in the temperature-rise curve
N o te 1 to entr y: S e e

Figure 2b.

3.6
areal heat diffusion time

A
are a with ti me - d i men s ion wh ich i s b ordere d b y the hori zonta l l i ne at the height o f the ma xi mu m
temp eratu re -ri s e and b y the temp eratu re -ri s e c u r ve

N o te 1 to entr y: S e e

Figure 2b.

3.7
heat diffusion time
τ0

time period beginning with pulse heating of the specimen front surface until time at which the specimen
temperature becomes uniform
τ0

=d

2

α

© ISO 2016 – All rights reserved

3


ISO 18555:2016(E)
where
τ0

is heat di ffusion time (s);

d

is thickness o f specimen (m);
is thermal di ffusivity (m 2 /s).

α

Note 1 to entry: See Figure 2b.

4 Principle

Thermal conductivities of the substrate, BC, and TC are determined according to calculations using
the thermal di ffusivities, specific heat capacities and bulk densities. The fundamental procedures are
shown in Figure 3.
The fundamental procedures for determining the thermal diffusivities of the substrate, BC, and TC

consist o f the measurement o f temperature-rise curves o f three types o f specimens (substrate, substrate
with BC, and substrate with TBC) by a flash method, and o f calculations. The thermal di ffusivities o f the
BC and TC are obtained by applying a multi-layer analytical model to the temperature-rise curves.
The specific heat capacities and bulk densities o f the substrate, BC, and TC are measured separately.

Figure 3 — Fundamental procedures for determining thermal conductivity

5 Apparatus for measuring thermal diffusivity

An example o f the apparatus for measuring the thermal di ffusivity is schematically shown in Figure 4.

The apparatus consists of the following.

5.1 Pulse heating light source.
5.2 Data recorder.
5.3 Measurement circuit.
5.4 Infrared radiometer.
4

© ISO 2016 – All rights reserved


ISO 18555:2016(E)

5.5

Specimen holder.

5.6

Chamber.

5.7

Thermocouple.

5.8

Temperature indicator.

T he app aratu s sh a l l b e s p e c i fie d accord i ng to I S O 1 8 75 5 : 2 0 0 5 and s hou ld b e c a l ibrate d u s i ng re ference

data and reference materials in reference to Annex E in ISO 18755:2005.

Key

1
2
3
4
5
6

F

pulse heating light source
data recorder
measurement circuit
infrared radiometer
trigger signal

7
8
9
10
11
12

amp lificatio n o f s ignal

i

g

u

r

e



4



—



T
y

p

i

c

a

l



a

p

p

a

r

a

t

u

s



temperature signal of specimen rear surface
specimen
specimen holder
chamber
thermocouple
temperature indicator

f

o

r



m

e

a

s

u

r

i

n

g



t

h

e



t

h

e

r

m

a

l



d

i

ff

u

s

i

v

i

t

y


a

c

c

o

r

d

i

n

g

t

o



a



f

l

a

s

h



m

e

t

h

o

d

6 Specimen
6.1

Shape and dimensions

The shape and dimensions of the specimen shall be as follows.
a)

T he th re e typ e s o f s p e c i men s (the s ub s trate, B C and T B C s p e c i men s) s ha l l b e u s e d .

Figure 5
Figure 6). The diameter or
side length of the specimen shall be from 10 × 10 m to 15 × 10 m.
c) The thicknesses of the substrate, BC and TC are given in Table 1.

b)

T he s p e ci men s hap e s ha l l b e a flat d i s k (

) or flat s qua re plate (

−3

d)

T he s ub s trate th ickne s s s ha l l b e the s ame

for

−3

the th re e typ e s o f s p e c i men s .

e) The thickness tolerance of substrate shall be ± 0,01 × 10 m.
f) The thickness of BC shall be the same for the BC and TBC specimens.
−3

© ISO 2016 – All rights reserved

5


ISO 18555:2016(E)

for the TBC specimen.

g)

T he d i fference b e twe en ma xi mu m and m i n i mu m th ickne s s sh a l l b e ≤ 0 , 01 d

h)

T he co ati ng s u r face s hou ld b e p ol i she d me chan ic a l ly i n order to s mo o th the co ati ng s u r face

j)

For

for

the

BC and TBC specimens.
i) The selections of the shape, the dimension and the thickness shall be decided according to the
agreement between parties involved in the transaction.
me a s urement

o f the

s p e c i fic

he at

of B C

c ap ac itie s

substrates shall be used as the specimen.

a) Substrate specimen

and

TC ,

the

b) BC specimen

co ati ngs

s tripp e d

o ff the

c) TBC specimen

Key

1 substrate
2 bond coat
3 top coat
diameter
S thickness of substrate
BC thickness of bond coat
TC thickness of top coat
D
d

d
d

F

i

g

u

r

e



5



—



S

a) Substrate specimen

h

a

p

e



o

f


f

l

a

t


d

i

s

k


s

p

e

c

i

m

e

n

s

b) BC specimen

c) TBC specimen

Key

1 substrate
2 bond coat
3 top coat
side length
S thickness of substrate
BC thickness of bond coat
TC thickness of top coat
l

d

d
d

F

6

i

g

u

r

e



6



—

S

h

a

p

e



o

f


f

l

a

t


s

q

u

a

r

e



p

l

a

t

e



s

p

e

c

i

m

e

n

s

© ISO 2016 – All rights reserved


ISO 18555:2016(E)
T

a

b

l

e



1

—



T

h

i

c

k

n

e

s

s

e

s



o

Designation
thickness of substrate
thickness of BC
thickness of TC
thickness of TBC specimen

S ymb ol

dS

dBC

dTC
d

f


s

u

b

s

t

r

a

t

e

,



B

C

,



a

n

d



T

C

Thickness (× 10 m)
−3

1,00 ≤

dS ≤ 2 , 0 0

0,15 dS dBC
0,20 (dS + dBC dTC
d = dS + dBC + dTC
≤

) ≤

≤ 3 ,00

6.2 Surface treatment
B o th s u r face s o f s p e ci men s

for

me a s uri ng therma l d i ffu s ivity sh a l l b e co ate d with a th i n, op aque,

pre ferably black layer accord i ng to I S O 1 8 75 5 : 2 0 0 5 .

7 Measuring procedure
7

.

1



S

p

e

c

i

m

e

n



t
h

i

c

k

n

e

s

s

The specimen thickness shall be measured as follows.
a) The specimen thickness shall be measured according to ISO 18755:2005.
b) The thickness of BC and TC shall be measured on the image of the coating cross section
according to ISO 1463.

7.2 Thermal diffusivity
7.2.1 Measurement of temperature-rise curve
According to ISO 18755:2005, the temperature-rise curve (Figure 2b) shall be measured as follows.
a) The specimen shall be placed in the specimen holder of the chamber. The BC and TBC specimens
f
and TC surfaces shall be detected (See Figure 2a).
b) The atmosphere is decided according to the agreement between parties involved in the transaction.
c) The temperature of the specimen rear surface before pulse heating, T0 , shall be measured with the
thermocouple.
d) With variation of the specimen temperature minimized (0,2 K or less per minute) before pulse
f
f
heating to measure the temperature rise.
s ha l l b e s o fi xe d that thei r s ub s trate s u r ace s a re he ate d b y pu l s e l ight a nd the temp eratu re s at B C

he ati ng a nd with the output o

i n rare d rad iome ter s tabi l i z e d; the s p e c i men i s s ubj e c t to pu l s e

7.2.2 Calculation of thermal diffusivity of substrate
T he d i ffu s ivity o f s ub s trate s ha l l b e c a lc u late d b a s e d on the temp eratu re -ri s e c u r ve o f the s ub s trate

specimen according to ISO 18755:2005.

7.2.3 Calculation of thermal diffusivities of BC and TC
The calculation of thermal diffusivities of BC and TC shall be made based on the temperature-rise curve

and with appl ic ation o f a mu lti-layer ana lytic a l mo del . T he a re a l he at d i ffu s ion ti me me tho d or the
the ore tic a l temp erature -ri s e c u r ve me tho d s ha l l b e u s e d as the mu lti-layer ana lytic a l mo del . T he mo del

shall be chosen according to the agreement between parties involved in the transaction.
© ISO 2016 – All rights reserved

7


ISO 18555:2016(E)

7.2.3.1

The areal heat diffusion time method (See Annex A)

a) Calculation of the areal heat diffusion time across the specimen.
The areal heat diffusion time shall be calculated as follows.
Either o f the following 1) or 2) may be used.

1) Calculation using numerical data of temperature-rise curve. The areal heat diffusion time, A

(hatched portion of Figure 2b) shall be determined directly from the data of temperature-rise curve.
2) Calculation using apparent thermal di ffusivity. Using the apparent thermal di ffusivity, α , the
areal heat diffusion time, A shall be calculated according to Formula (1).
A = d 2 6α app
(1)
app

(

)

where
is thickness o f specimen (m);

d

/s).
The apparent thermal di ffusivity o f the specimen, αapp , shall be calculated according to equiareal
method or half-time method (see ISO 18755:2005).
3) The correction factors for heat loss and non-uniform heating should be calculated in reference to
αapp is apparent thermal di ffusivity o f specimen (m 2

Annexes B and D respectively in ISO 18755:2005.

b) Calculation of thermal diffusivities of substrate, BC, and TC.
1) The thermal di ffusivity o f BC shall be calculated according to Formulae (2) and (3) on the
basis o f the measurement made using the BC specimen, and the thermal di ffusivity o f substrate

obtained in 7.2.2.

The thermal di ffusivity o f BC can be expressed as follows:

=d

α BC

2

BC

(2)

/ τ BC

where
αBC

is thermal di ffusivity o f BC (m 2 /s);

dBC is thickness o f BC (m);

is heat diffusion time of BC (s).
6 (c ρ d + c ρ d ) A
− ( c ρ d + 3c
=
3c ρ d + c ρ d

τBC
τ BC

where

S

S

BC

BC

BC

BC-S

S

S

S

S

BC

S

S

BC

BC

)

ρ BC dBC ( dS / α S )
2

(3)

BC

ρs

is specific heat capacity o f substrate [J/(kg·K)];
is bulk density o f substrate (kg/m 3 );

αs

is thermal di ffusivity o f substrate (m 2 /s);

cs

8

S

© ISO 2016 – All rights reserved


ISO 18555:2016(E)

ds

i s th ickne s s o f s ub s trate (m) ;

cBC

i s s p e ci fic he at c ap ac ity o f B C [ J/( kg· K) ] ;

ρ BC

i s bu l k den s ity o f B C ( kg/m

A BC-S

3

);

is areal heat diffusion time of BC specimen (s).

2 ) T he therma l di ffus ivity o f TC sha l l b e calcu lated accordi ng to Formulae (4) and (5 ) on the b as i s o f

the measurement made using the TBC specimen, αs obtained in 7.2.2 and αBC obtained in Formula (2).
T he therma l d i ffu s ivity o f TC ca n b e e xpre s s e d a s

α TC

2
= d TC

fol lows:

(4)

τ TC

where
αTC

i s therma l d i ffu s ivity o f TC (m

dTC

i s th ickne s s o f TC (m) ;

τTC

2

/s) ;

is heat diffusion time of TC (s).





 6 ( c S ρ SdS + c BC ρ BCdBC + c TC ρ TCd TC ) A TBC-S






 
2 

1
 −  3c ρ d + c ρ d + 3c ρ d + 6c S ρ SdSc TC ρ TCd TC  dBC 
τ TC =
BC BC BC
TC TC TC
 α BC 
c B C ρ BC d BC
3c S ρ S d S + 3 c BC ρ BC d BC + c TC ρ TC d TC   S S S






2
dS

 c ρ d 3c ρ d
 − ( S S S + BC BC BC + 3c TC ρ TC d TC ) α



S

(5)

where
cTC

i s s p e c i fic he at c ap acity o f TC [ J/( kg· K ) ] ;

ρ TC

i s bu l k den s ity o f TC ( kg/m

ATBC-S
7.2.3.2

3

);

is areal heat diffusion time of TBC specimen (s).

Calculation using theoretical temperature-rise curve method

T he therma l di ffu s ivitie s o f B C a nd TC s ha l l b e c a lc u l ate d b y applyi ng the the ore tic a l temp eratu re -ri s e
c u r ve b a s e d on a mu lti-l ayer mo del ana lys i s to the me a s u re d temp eratu re -ri s e c ur ve .

The theoretical temperature-rise curve shall be chosen according to the agreement between parties
involved in the transaction. Examples of the theoretical temperature-rise curve are given in Annex B.
The measured temperature-rise curve should be corrected for heat loss and non-uniform heating in
reference to ISO 18755:2005 (Annexes B and D

re s p e c tively) .

a)

C a lc u l ation o f therma l d i ffu s ivity o f B C .

1) The theoretical temperature-rise curve of the BC specimen is given in Formula (6).
© ISO 2016 – All rights reserved

9


ISO 1 85 5 5 : 2 01 6(E)

(6)

T t ∆T) th = F(dS , d BC , α S , α BC , c S , c BC , ρ S , ρ BC , t)

( ( )/

where

(T(t

) /Δ

T

) th

i s the ore tic a l temp eratu re -ri s e c u r ve;

is a function.

F

2 ) I nput the d ata e xcep t

3)

T he

therma l

for

the therma l d i ffu s ivity o f B C i nto th i s e quation .

d i ffu s ivity o f B C

s ha l l

be

temperature-rise curve of the BC specimen.

b)

c a lc u late d

b y fitti ng th i s

e quation

to

the

me as u re d

C a lc u lation o f therma l d i ffu s ivity o f TC .

1) The theoretical temperature-rise curve of the TBC specimen is given in Formula (7).
Tt

(7)

T = G(d , d , d , α , α , α , c , c , c , ρ , ρ , ρ , t )

( ( ) / ∆ ) th

S

BC

TC

S

BC

TC

S

BC

TC

S

BC

TC

where G is a function.
2 ) I nput the data excep t

3)

T he

therma l

for

the therma l d i ffu s ivity o f TC i nto th i s e quation .

d i ffu s ivity o f TC

s ha l l

be

c a lc u l ate d

temperature-rise curve of the TBC specimen.

b y fitti ng th i s

e quation

to

the

me as u re d

7.3 Specific heat capacity
T he s p e ci fic he at c ap ac ity s ha l l b e de term i ne d a s

me as u rement

of

a)

T he

b)

T he l i teratu re va lue s

ASTM E1269 11.

the

fo r

s p e ci fic

he at

fol lows .

c ap ac ity

sh a l l

be

accord i ng

to

EN

82 1-3 : 2 0 0 5

or

the co ati ng p ro duce d b y the s a me co ati n g p ro ce s s wi th the p o wder o f

the same composition should be used, if the preparation of the coating stripped off the substrate

i s d i ffic u lt.

NOTE The value measured for the raw material powders of the respective coating can be used, when the
literature values are not available.
7.4 Bulk density

The substrate, BC, and TBC specimens shall be used as follows for determining the bulk densities of BC
and TC.
a) Measure the mass of the substrate, BC and TBC specimens.
b)

M e a s u re the d i men s ion s o f the s ub s trate, B C and T B C s p e c i men s b y u s i ng the m ic rome ter and

c)

T he

d)

T he bu l k den s ity o f B C sha l l b e de term i ne d accord i ng to Formu la (8) .

calculate their volumes.

bu l k den s ity o f s ub s trate

substrate specimen.
ρ BC

=

(ρ (

where ρBC-S
e)

10

BC-S

d

S

+ dBC ) − ρ S dS

)

s ha l l

d

be

de term i ne d u s i ng the

ma s s

d i men s ion s

o f the

(8)

BC

i s bu l k den s ity o f the B C s p e ci men ( kg/m

and the

3 ).

T he bu l k den s ity o f TC sha l l b e de term i ne d accord i ng to Formu la (9) .

© ISO 2016 – All rights reserved


ISO 18555:2016(E)

ρ TC

=

( ρ (d + d

where ρTBC-S

TBC-S

s

BC

+ d TC ) − ρ s d s − ρ BC dBC

)d

i s bu l k den s ity o f the T B C s p e ci men ( kg/m

(9)

TC

3 ).

8 Thermal conductivities of BC and TC

Thermal conductivities of BC, λBC, , and TC, λTC,
(11):

, s ha l l b e de term i ne d re s p e c tively b y Formu lae (10) a nd

λ BC = α BC c BC ρ BC

(10)

λTC = α TCcTC ρ TC

(11)

9 Report
9.1

Items to be reported

T he rep or t sh a l l contai n the

described in the report.
a) Specimen:

fol lowi ng

item s .

When the rep or te d va lue s

are c ite d ,

they s hou ld b e

1)

materi a l o f s ub s trate;

2)

materi a l s and s prayi ng cond ition s o f B C and TC , i nclud i ng s u r face prep a ration o f the s ub s trate;

3)

s hap e o f the s p e ci men (d i s k or s quare plate) ;

4)

d i ame ter or s ide leng th o f the s p e ci men;

5) thickness of substrate, BC and TC.
b) Measurement conditions:
1)

typ e o f the app a ratu s

2)

atmo s phere

for

for

me as u ri ng the therma l d i ffu s i vity (mo del o f the i n s tru ment) ;

me a s u ri ng the temp eratu re -ri s e c u r ve;

3) surface treatment of the specimen for measuring the temperature-rise curve (coating material,
co ati ng pro ce du re) ;

4) temperature of specimen rear surface before pulse heating, T0
5)

c a lc u lation me tho d o f the therma l d i ffu s ivity;

6)

me tho d

for

;

me a s u ri ng the s p e c i fic he at c ap acity.

c) Results of measurement and calculation:
1)

bu l k den s itie s o f s ub s trate, B C and TC;

2)

s p e ci fic he at c ap ac itie s o f s ub s trate, B C a nd TC;

3)

therma l d i ffu s i vitie s o f s ub s trate, B C and TC;

4) thermal conductivities of substrate, BC and TC.

© ISO 2016 – All rights reserved

11


ISO 18555:2016(E)

9.2
T he

Additional items to be selected for the report
rep or t

may

contai n

add itiona l

item s .

T he

add itiona l

item s

a re

according to the agreement between parties involved in the transaction.

a)

ye ar/month/day o f me as u rement and the me as u rement l ab orator y;

b)

manu fac turer o f the me a s uri ng s ys tem;

c)

de tai l s o f therma l d i ffu s ivity me a s urement;

1) correction factors used in 7.2.3.1a) and 7.2.3.2

s ele c te d

from

the

fol lowi ng ,

;

2)

typ e o f thermo couple and p o s itiona l relation sh ip b e twe en the thermo couple and s p e ci men;

3)

typ e o f the i n fra re d rad iome ter;

4)

pu l s e he ati ng l ight s ou rce (typ e, i nten s ity, pu l s e width, pu l s e b e am centre o f gravity a nd the
me tho d to de term i ne the centre o f gravity) ;

5)

nu mb er o f the me as u rement;

6)

data re gard i ng the temp eratu re -ri s e c ur ve (the repre s entative data i n c as e o f ne ce s s ity) ;

7) half-rise time or areal heat diffusion time.

12

© ISO 2016 – All rights reserved


ISO 18555:2016(E)

Annex A

(informative)
Areal heat diffusion time method

A.1 General

A multi-layer model is shown in Figure A.1 . According to the multi-layer model, based on the response
function method,[2] the areal heat diffusion time A [s] across the multi-layer specimen is expressed as:

A=

∫

∞

 1 − b τ ⋅ T (t ) dt =


r

0

where

lim
ξ

→0

 1

−
b
τ ⋅ T? (ξ ) 
 ξ


r

b

is thermal e ffusivity across the multi-layer specimen;

τ

is heat di ffusion time across the multi-layer specimen;

Tr (t) = T(t) / ∆Τ

is normalized temperature rise (see 3.3 );

T?r

(

ζ

)=

∞

∫ ()
0

Tr t

exp

(−ζ t) dt

ξ

(A.1)

is Laplace transform of Tr(t);
is a Laplace parameter.

The heat diffusion across the n -layered specimen is systematically analysed using Formula (A.1).

© ISO 2016 – All rights reserved

13


ISO 18555:2016(E)

Key
1 pulse heating
2 infrared radiometer
di thickness of the i th layer (i = 1,2,…, n )
αi
ci

ρi
bi

τi

thermal di ffusivity o f the i th layer (i = 1,2,…, n )
specific heat capacity o f the i th layer (i = 1,2,…, n )
bulk density o f the i th layer (i = 1,2,…, n )
thermal e ffusivity o f the i th layer (i = 1,2,…, n )
heat diffusion time of the i th layer (i = 1,2,…, n )

Figure A.1 — Multi-layer model

A.2 Single-layer model

The areal heat di ffusion time across a single-layer specimen A1-S is expressed as:
A1 -S

=τ

1

(A.2)

/6

From Formula (A.2), the heat di ffusion time o f the first layer is determined by Formula (A.3):
τ1

(A.3)

= 6 A1 -S

A.3 Two-layer model

The areal heat di ffusion time across a two layer specimen A 2-S is expressed as:
A2 -S

=

b1τ 13/ 2

+ 3 b2τ 1τ 21 /2 + 3 b1τ 11/2τ 2 + b2τ 23/2
6 b1 τ 1 + b 2 τ 2

(

(A.4)

)

From Formula (A.4), the heat di ffusion time o f the 2nd layer is determined by Formula (A.5):
τ2

=

(

6 A2 -S c1 ρ 1 d1

+ c ρ d ) − ( c ρ d + 3c ρ d ) τ
3c ρ d + c ρ d
2

1

14

2 2

1 1

1

2

1 1

2

2 2

1

(A.5)

2 2

© ISO 2016 – All rights reserved


ISO 18555:2016(E)

A.4 Three-layer model

The areal heat di ffusion time across a three layer specimen A 3-S is expressed as:


 b τ (τ + 3τ + 3τ ) + b τ
=
1

A

3 -S

1

1

2

3

2

2

3

6

(A.6)


+ τ + 3τ ) + b τ (3τ + 3τ + τ ) + b b τ τ τ 
b

b τ +b τ +b τ

(τ

(

3

1

1

2

1

3

1

2

3

2

3

3

3

)

1

2

3

1 2

1 2

1 2

1

2

3

2

From Formula (A.6), the heat di ffusion time o f the 3rd layer is determined by Formula (A.7):

τ

3

=

3

1

+ 3c ρ d + c ρ d

3c1 ρ 1 d1

2


 6 A − S ( c ρ d + c ρ d + c ρ d ) − ( c ρ d + 3c ρ d + 3c ρ d ) τ

 
 −  3c ρ d + c ρ d + 3c ρ d + 6c ρ d c ρ d  τ
 

cρd


2

2

3

3

3

1

1

1

2

2

2

3

3

3

1

1

1

1

1

2

2

2

3

3

1

1

2

3

3

2

2

3

3

3

1

3

2

3

2

(A.7)

1

1

2

2

A.5 Thermal diffusivity

The thermal di ffusivity o f each layer α is determined by Formula (A.8):
i

αi

= d i2 / τ i ,

(

i = 1, 2, 3)

(A.8)

A.6 Convenient calculation method of areal heat diffusion time [3] [4]

By considering the temperature-rise curve o f a two or a three-layer specimen as that o f a single-layer

specimen, the areal heat diffusion time is assumed as follows:
A =

( d1

+d
6α

2 -S

2

)

2

(A.9)

app

where αapp is apparent thermal di ffusivity of a two-layer specimen.
A3 -S

=

(

d1

+ d 2 + d3 ) 2
α app

6

(A.10)

where αapp is apparent thermal di ffusivity of a three-layer specimen.
This is a simple technique and has advantages practically, although it is an approximation.

© ISO 2016 – All rights reserved

15











ISO 18555:2016(E)

Annex B

(informative)
Examples of theoretical temperature-rise curves

B.1 General
Repre s entative e xample s o f the the ore tic a l temp eratu re -ri s e c u r ve s b as e d on a mu lti-layer mo del (s e e

Figure A.1
The theoretical temperature-rise curve is chosen according to
the agreement between parties involved in the transaction.
) ana lys i s a re given b elow. [5 ]

B.2 Two-layer model





 γ 2 ⋅ t 
(ω1 X1 + ω 2 X2 ) exp  −  dk 2  
  2  

  α 2  
 T (t ) 
∞
  
  = 1 + 2
 ∆T 
k=1 ω 1 X1 cos (ω 1γ k ) + ω 2 X 2 cos (ω 2γ k )
th
where

∑

X1

2
= ρρ 1 cc1 dd1 ⋅ d22α 1 + 1 , ω =

X2 =

2 2 2

d1 α 2

ρ 1 c 1 d1
ρ 2c 2d2

d22α 1
d12α 2

⋅

1

−1 , ω =
2

d12α 2
d22α 1

+1

d12α 2
d22α 1

−1

(B.1)

γk i s defi ne d b y the k-th positive root of following equation:

( ) + X (ω γ ) = 0

X1 sin ω1γ

2

sin

2

B.3 Three-layer model





 γ 2 ⋅ t 
(ω1 X1 + ω 2 X2 + ω3 X3 + ω 4 X4 ) exp  −  dk 2  
  3  
  α  
 T (t ) 
∞
  3  
  = 1 + 2
(B.2)
 ∆T 
ω 1 X1 cos (ω 1γ k ) + ω 2 X2 cos (ω 2γ k ) + ω 3 X3 cos (ω 3γ k ) + ω 4 X 4cos (ω 4γ k )
k
1
=
th
where

∑

2
2




X =  ρ c d . d22α 1 + 1   ρ c d . d32α 2 + 1  ….. ω

 ρ c d d1α 2
  ρ c d d 2α 3
1

1

1

2

2

2

2

2

2

3

3

3

1

16

1

=

d12α 3
d22α 3
+
+1
d32α 1
d32α 2

© ISO 2016 – All rights reserved


ISO 1 85 5 5 : 2 01 6(E)


 ρ c d d 22α 1
  ρ c d d32α 2
X =
. 2 + 1 
. 2 − 1  ….. ω

 ρ c d d1α 2
  ρ c d d 2α 3




 ρ c d d 22α 1
  ρ c d d32α 2

X =
. 2 −1 
. 2 − 1  ….. ω
 ρ c d d1α 2
  ρ c d d 2α 3





 ρ c d d 22α 1
  ρ c d d 32α 2
X =
. 2 −1 
. 2 + 1  ….. ω

 ρ c d d1α 2
  ρ c d d 2α 3



1

1

1

2

2

2

2

2

2

3

3

3

1

1

1

2

2

2

2

2

2

3

3

3

1

1

1

2

2

2

2

2

2

3

3

3

2

3

2

3

4

4

γk i s defi ne d b y the k-th positive root of the following:

=

d12α 3
d22α 3
+
−1
d32α 1
d32α 2

=

d12α 3
d22α 3
+ 2 +1
d32α 1
d3 α 2

=

d12α 3
d22α 3
+ 2 −1
d32α 1
d3 α 2

X1 sin ( ω1γ ) + X2 sin ( ω2γ ) + X3 sin ( ω3γ ) + X4 sin ( ω 4γ ) = 0

© ISO 2016 – All rights reserved

17


ISO 18555:2016(E)

Bibliography
[1]

ISO 14188:2012, Metallic and other inorganic coatings — Test methods for measuring thermal cycle

[2]

B aba T Analysis o f One-dimensional Heat Di ffusion a fter Light Pulse Heating by the Response
Function Method. Jpn. J. Appl. Phys. 2009, 4805EB04

[3]

A koshim a M., Tanaka T., E ndo S., B aba T., H arada Y., Kojim a Y. et al Thermal Di ffusivity
Measurement for Thermal Spray Coating Attached to Substrate Using Laser Flash Method. Jpn. J.
Appl. Phys. 2011, 5011RE01

[4]

resistance and thermal shock resistance for thermal barrier coatings

Takah ashi S., A koshim a M., Tanaka T., E ndo S., O gawa M., Kojim a Y. et al Determination of
Thermal Conductivity o f Thermal Barrier Coatings, Proc. The 5th Asian Thermal Spray Conference,

2012, pp 11-12

[5]

A raki , N., M akino , A., I shiguro , T., M ih ara , J . An Analytical Solution o f Temperature Response
in Multilayered Materials, for Transient Methods, International Journal of Thermophysics, 13-3

(1992) pp 515-538.

18

© ISO 2016 – All rights reserved